It can be seen from the stress distribution of a loaded beam
that the greatest stress occurs at the top and bottom extrem
ities of the beam.

This led to the improvement on a rectangular section by
introducing the l-section in which the large flanges were
situated at a distance from the neutral axis. In effect, the
flanges carried the bending in the form of tension stress in one
flange and compression stress in the other, while the shear was
carried by the web.

For these situations where bending is high but shear is low,
for example in roof design, material can be saved by rising a
framework design. A truss is a pinpointed framework.

A truss concentrates the maximum amount of materials as far
away as possible from the neutral axis. With the resulting
greater moment arm (h), much larger moments can be resisted.

Resistance of a truss at a section is provided by:

M = C x h = T x h, where C = T in parallel cords and:

C = compression in the top chord of the truss.

T = tension in bottom chord of a simply supported truss.

h = vertical height of truss section.

If either C, T or h can be increased, then the truss will be
capable of resisting heavier loads. The value of h can be
increased by making a deeper truss.

Allowable C or T stresses can be increased by choosing a
larger cross section for the chords of the truss, or by changing
to a stronger material.

A framework or truss can be considered as a beam with the
major part of the web removed. This is possible where bending
stresses are more significant than shear stresses. The simple
beam has a constant section along its length, yet the bending and
shear stresses vary. The truss, made up of a number of simple
members, can be fabricated to take into account this change in
stress along its length.

The pitched-roof truss is the best example of this, although
the original shape was probably designed to shed rain water. Roof
trusses consist of sloping rafters which meet at the ridge, a
main tie connecting the feet of the rafters, and internal bracing
members. They are used to support a roof covering in conjunction
with purling, which are members laid longitudinally across the
rafters, the roof covering being attached to the purling. The
arrangement of internal bracing depends on the span. Rafters are
normally divided into equal lengths, and ideally, the purlins are
supported at the joints, so that the rafters are only subjected
to axial forces. This is not always practicable, since purlin
spacing is dependent on the type of roof covering. When the
purlins are not supported at the panel joints, the rafter members
must be designed for bending as well as axial force. See Figure
4.5.

The internal bracing members of a truss should be triangulated
and, as far as possible, be arranged so that long members are in
tension and compression members are short to avoid buckling
problems.

The outlines in Figure 4.6 give typical forms for various
spans. The thick lines indicate struts.

The lattice girder, also called a truss, is a plane frame of
open web construction, usually having parallel chords or booms at
top and bottom. There are two main types, the N (or Pratt) girder
and the Warren girder. They are very useful in long-span
construction, in which their small depth-to-span ratio, generally
about 1/10 to 1/14, gives them a distinct advantage over roof
trusses.

Steel and timber trusses are usually designed assuming
pin-jointed members. In practice, timber trusses are assembled
with bolts, nails or special connectors, and steel trusses are
bolted, riveted or welded. Although these rigid joints impose
secondary stresses, it is seldom necessary to consider them in
the design procedure. The following steps should be considered
when designing a truss:

1 Select general layout of truss members and truss
spacing.

2 Estimate external loads to be applied including self
weight of truss, purlins and roof covering, together with
wind loads.

5 Select material and section to produce in each member a
stress value which does not exceed the permissible value.
Particular care must be taken with compression members
(struts), or members normally in tension but subject to
stress reversal due to wind uplift.

Unless there are particular constructional requirements, roof
trusses should, as far as possible, be spaced to achieve a
minimum of weight and economy of materials used in the total roof
structure. As the distance between trusses is increased, the
weight of the purlins tends to increase more rapidly than that of
the trusses. For spans up to about 20m, the spacing of steel
trusses is likely to be about 4m, and in the case of timber, 2m.

The pitch, or slope, of a roof depends on locality, imposed
loading and type of covering. Heavy rainfall may require steep
slopes for rapid drainage; a slope of 22° is common for
corrugated steel and asbestos roofing sheets. Manufacturers of
roofing material usually make recommendations regarding suitable
slopes and fixings.

To enable the designer to determine the maximum design load
for each member, the member forces can be evaluated either by
calculation or graphical means, and the results tabulated as
shown:

Member

Dead

Load

D

Imposed

Load

I

Dead + Imposed

Load

D+l

Wind

Load

W

Design

Load

A simplified approach can he used if the intention is to use a
common section throughout. Once the layout has been chosen, the
member which will carry the maximum load can be established. An
understanding of the problems of instability of compression
members will lead the designer to concentrate on the top chord or
rafter members. A force diagram or method of sections can then be
used to determine the load on these members, and the necessary
size.

Example 23

A farm building comprised of block walls carries steel roof
trusses over a span of 8m. Roofing sheets determine the purlin
spacings.

Assume a force analysis shows maximum rafter forces of
approximately 50kN in compression (D + 1) and 30kN in tension (D
+ W), outer main tie member 50kN tension (D + 1) and 30kN
compression (D + W). A reversal of forces due to the uplift
action of wind will cause the outer main tie member to have 50kN
of tension and 30kN of compression.

Consulting a structural engineering handbook reveals that a
steel angle with a section of 65mm x 50mm x 6mm and an effective
length of 1.8m can safely carry 29kN in compression.

Rafter: Using two angles back-to-back will be
satisfactory, since distance between restraints is only 1.38m.
(Note angles must be battened together along the length of the
rafter).

Main Tie: The 65mm x 50mm x 6mm section can carry the
required tensile force. Although its length is a little greater
than 1.8m, the compressive load brought about by the uplift of
the wind is safe since the design codes allow a greater
slenderness ratio for intermittent loads such as wind.

Finished Design: Note the use of a sole plate to
safely distribute the load to the blockwork wall, so that the
bearing stress of the blocks is not exceeded. See Figure 4.7.

Apart from the roof truss, there are a number of other
structural frames commonly used in farm building construction.
They include portal frames, pole barns, and postand-beam frames.

A single-bay portal frame consists of a horizontal beam or
pitched rafters joined rigidly to vertical stanchions on either
side to form a continuous plane frame. For the purposes of
design, portal frames can be classified into three types: fixed
base, pinned base (2 pins), pinned base and ridge (3 pins).

The rigid joints and fixed bases have to withstand bending
moments and all bases are subjected to horizontal as well as
vertical reactions. Hence foundation design requires special
attention. The externally applied loads cause bending moments,
shear forces and axial forces in the frame.

Portal frames are statically indeterminate structures and the
complexity of the analysis precludes coverage here. However, the
results of such calculations for a number of standard cases of
loading are tabulated in handbooks. Using these and the principle
of superposition, the designer can determine the structural
section required for the frame. Determining the maximum values of
the bending moment, shear force and axial force acting anywhere
in the frame; allows the selection of an adequate section for use
throughout the frame. Care must be exercised to ensure that all
joints and connections are adequate.

Portal frames may be made of steel, reinforced concrete or
timber. With wider spans the structural components become massive
if timber or reinforced concrete is used. Hence, steel frames are
most common for spans over 20m. At the eaves, where maximum
bending moments occur, the section used will need a greater depth
than at other points in the frame.

Pole barns are usually built with a relatively simple
foundation, deeper than usual, and backfilled with rammed earth.
Pole barns are braced between columns and rafters in each
direction. The braces serve to reduce the effective length of
compression members and the effective span of rafters and other
beam members. This leads to a structure which is simple to
analyze and design, and can be a lowcost form of construction.

A shed type building is a simple construction consisting of
beams (horizontal or sloping), supported at their ends on walls
or posts. There may be one or more intermediate supports
depending on building width. Purlins running longitudinally
support the roof covering. As the principle members are simple or
continuous beams, (very often timber of rectangular section), the
stress analysis aspect of the design is straight forward. When
the beam is supported by timber posts, the post design is not
difficult since the load is assumed to be axial. Like the poles
in the pole barn, the foundation can consist of a simple pad of
concrete beneath the post, or the base of the post can be set
into concrete.

The methods used to join members include lapped and butt
connectores. Bolt and connector joints, nailed joints and glued
joints and sometimes a combination of two are examples of lapped
connections. Butt connections require the use of plates or
gussets. In all cases the joints should be designed by
calculating the shear forces that will occur in the members.

If two members overlap the joint is called a single-lap joint.
If one is lapped by two other members, i.e., sandwiched between
them, it is called a double-lap joint.

With a single lap the joint is under eccentric loading. For
small-span trusses carrying light loads, this is not significant,
but when the joints carry large loads eccentricity should be
avoided by the use of double-lap joints. Double members are also
used to obtain a satisfactory arrangement of members in the truss
as a whole.

Sandwich construction enables the necessary sectional area of
a member to be obtained by the use of relatively thin timbers,
any double members in compression being blocked apart and fixed
in position to provide the necessary stiffness.

Butt Joints

The use of gussets permits members to butt against each other
in the same plane, avoids eccentric loading on the joints and
provides, where necessary, greater joining area than is possible
with lapped members. This is often an important factor in nailed
and glued joints. Arrangement of members on a single centre line
is usually possible with gussets.

When full-length timber is not available for a member, a butt
joint with cover plates can be used to join two pieces together.
This should be avoided, if possible, for the top members
(rafters) of a truss and positioned near mid-span for the bottom
member (main tie).

Simple bolted joints should only be used for lightly loaded
joints, since the bearing area at the hole (hole diameter times
member thickness) and the relatively low bearing stress allowed
for the timber compared with that of the steel bolt, may cause
the timber hole to elongate and fail.

Timber connectors are metal rings or toothed plates used to
increase the efficiency of bolted joints. They are embedded half
into each of the adjacent members and transmit load from one to
the other. The type most commonly used for light structures is
the toothed-plate connector, a mild-steel plate cut and stamped
to form triangular teeth projecting on each side that embed in
the surfaces of the members up on tightening the bolt which
passes through the joint. The double-sided toothed connector
transmits the load and the bolt is assumed to take no load.

Glued Joints

Glues made from synthetic resins produce the most efficient
form of joint, as strong as or even stronger than the timber

joined, and many are immune to attack by dampness and decay.
With this type of joint all contact surfaces must be planed
smooth, and the necessary pressure provided during setting of the
glue. Bolts or nails which act as cramps are often used and left
in place.

The members may be glued directly to each other using lapped
joints or single-thickness construction may be used by the
adoption of gussets. As with nailed joints, lapped members may
not provide sufficient gluing area and gussets must then be used
to provide the extra area.

Glued joints are more often used when trusses are
prefabricated because control over temperature, joint fit and
clamping pressure is essential. For home use glue is of the used
together with nail joints.

Joining by nails is the least efficient of the three methods
referred to, but is an inexpensive and simple method, and can be
improved upon by using glue in combination with the nails.

When trusses are pre-fabricated in factories, nailing plates
are often used to connect the member. These fasteners come in two
types:

1 A thin-gauge plate called a pierced plate fastener, which
has holes punched regularly over its surface to receive nails.
The pierced plate can also be used for on-site fabrication.

2 A heavier plate with teeth punched from the plate and bent
up 90 degrees, called a toothed-plate fastener, or connector. The
type, in which the teeth are an integral part of the plate, must
be driven in by a hydraulic press or roller.

In order to permit the development of the full load at each
nail, and to avoid splitting of the wood, minimum spacings
between nails and distances from the edges and ends of the member
are necessary.

Nailing patterns for use on timber structures are usually
available locally. They are dependent on the quality and type of
nails and timber used, and are based on the safe lateral nail
load.

The Housing Research and Development Unit of the University of
Nairobi investigated timber nailed joints made with spacings in
accordance with the continental standard for timber joints, which
proved to be satisfactory. The main principles are given in table
4.9 and 4.10.

Connections may be bolted, riveted or welded. The principal
design considerations are shear, tension and compression, and the
calculations are relatively straightforward for the types of
design covered.

Nailing
area

x

ro

dl

d11

rb

e0

eb

0

5d

5d

10d

5d

-

I5d

10

5d

5d

10d

5.5d

8d

15d

20

5d

5d

10d

6d

8d

I5d

30

5d

5d

10d

6.5d

8d

15d

40

5d

5d

10d

7d

8d

15d

50

5d

5d

10d

7.5d

8d

15d

£
60

5d

5d

10d

8d

8d

15d

d: Diameter of nail mm.

r0: Distance from extreme row of nails to unloaded
edge of member.

d1: Distance between two nails in nailing area,
measured perpendicular to axis of member.

d11: Distance between two nails measured parallel
to axis of member.

rb: Distance from extreme row of nails to loaded
edge of member.

e0: Distance from the nearest row of nails to the
unloaded end of member.

eb: Distance from the nearest row of nails to the
loaded end of member.

Stability problems in a building are due mainly to horizontal
loads such as those resulting from wind pressure, storage of
granular products against walls, soil pressure against
foundations, and sometimes earthquakes.

Overturning of foundation walls and foundation piers and pads
is counteracted by the width of the footing and the weight of the
structure. Only in special cases will it be necessary to give
extra support in the form of buttresses.

Overturning of external walls is counteracted by the support
of perpendicular walls and partitions. Note however, that not all
types of walls, for example framed walls, are adequately rigid
along their length without diagonal bracing. If supporting walls
are widely spaced and/ or the horizontal loads are large, extra
support can be supplied by the construction of piers, columns or
buttresses. See Chapter 5.

Diagonal bracing is used to make framed walls and structures
stiff. Long braces should preferably transfer the load with a
tensile stress to avoid buckling. Braces are usually supplied in
pairs, i.e., on both diagonals, so that one will always be in
tension independent of wind direction.

If the framed wall is covered with a sheet material, like
plywood, chipboard or metal sheets, the lateral forces on the
frame can be counteracted by shear in the sheets. This design
requires that the sheets to be securely fixed to the frame, both
horizontally and vertically. The sheets must also be strong
enough to resist buckling or failure through shear.

Masonry and concrete walls which are stiff and capable of
resisting lateral wind loading are called shear walls.

Portal or rigid frame buildings are normally stable laterally,
when the wind pressure acts on the long sides. However, when the
wind loads occur at the gable ends, the frames may need extra
support from longitudinal bracing. Tension rods are frequently
used.

Post-and-beam or shed-frame buildings will, in most cases,
require wind bracing, both along and across the building since
there are no rigid connections at the top of the wall to transfer
loads across and along the building. The same applies to
buildings employing roof trusses. End bracing should be
installed.

Walls with long spans between the supporting crosswalls,
partitions or buttresses tend to bend inwards due to wind load or
outwards if bulk grain or other produce is stored against the
wall. At the bottom of the wall this tendency is counteracted by
the rigidity of the foundation (designed not to slide) and the
support of a floor structure. The top of the wall is given
stability by the support of the ceiling or roof structure or a
specially designed wall beam which is securely anchored to the
wall.

The designer must consider the ability of the building to
withstand horizontal loading from any and all directions, without
unacceptable deformation.